I have downloaded d4x download manager program but I do not know its dpendencies. I tried to install the single deb file with "Gdebi Package installer" but it showed an error of dependency. I downloaded that file too which itself could not be installed due to the same problem. The method of one by one file downloading was exhausting.
Is there any program that accepts "d4x_2.5.7.1-5_amd64.deb" as input and givres me a full list of dependencies that must be saitisfied proior to installing the program with a single click? I want to give that list to another download manager.

that is not a good idea.
dpkg -i <package> will install .deb files that are not in the archive. if it sees dependencies unfullfilled it will say so (as it does not resove these by itself).apt-get -f install will try to satisfy these dependencies.
that said in general, listen to Hesaid in this case. and do yourself a favour and do not install ubuntu stuff on aptosid or debian. you might regret it.
besides that: wget can probably do anything you ask from a download manager.